The bus from Belfast International Airport takes you to Gt Victoria St. If you then want to get a bus to PRONI, you need to walk round to the City Hall (5 mins) and get a bus from there. (Several different bus numbers go to PRONI. There’s an info point at the City Hall bus stand and they’ll direct you.) Or you can get the train from Gt Victoria St (the bus and train stations are in the one building) to Titanic station which is a 5 mins walk from PRONI. (Bangor line trains).
Be aware that if you have luggage, you’ll need to store it somewhere before you get to PRONI. PRONI have lockers for coats and jackets but they can’t accommodate suitcases and you can’t take them into the search rooms.